Detailed syntax breakdown of Definition df-gzinf
| Step | Hyp | Ref
| Expression |
|---|
| 1 | | cgzi 31348 |
. 2
class
AxInf |
| 2 | | c0 3915 |
. . . . 5
class
∅ |
| 3 | | c1o 7553 |
. . . . 5
class
1𝑜 |
| 4 | | cgoe 31315 |
. . . . 5
class
∈𝑔 |
| 5 | 2, 3, 4 | co 6650 |
. . . 4
class
(∅∈𝑔1𝑜) |
| 6 | | c2o 7554 |
. . . . . . 7
class
2𝑜 |
| 7 | 6, 3, 4 | co 6650 |
. . . . . 6
class
(2𝑜∈𝑔1𝑜) |
| 8 | 6, 2, 4 | co 6650 |
. . . . . . . 8
class
(2𝑜∈𝑔∅) |
| 9 | | cgoa 31329 |
. . . . . . . 8
class
∧𝑔 |
| 10 | 8, 5, 9 | co 6650 |
. . . . . . 7
class
((2𝑜∈𝑔∅)∧𝑔(∅∈𝑔1𝑜)) |
| 11 | 10, 2 | cgox 31334 |
. . . . . 6
class
∃𝑔∅((2𝑜∈𝑔∅)∧𝑔(∅∈𝑔1𝑜)) |
| 12 | | cgoi 31330 |
. . . . . 6
class
→𝑔 |
| 13 | 7, 11, 12 | co 6650 |
. . . . 5
class
((2𝑜∈𝑔1𝑜)
→𝑔
∃𝑔∅((2𝑜∈𝑔∅)∧𝑔(∅∈𝑔1𝑜))) |
| 14 | 13, 6 | cgol 31317 |
. . . 4
class
∀𝑔2𝑜((2𝑜∈𝑔1𝑜)
→𝑔
∃𝑔∅((2𝑜∈𝑔∅)∧𝑔(∅∈𝑔1𝑜))) |
| 15 | 5, 14, 9 | co 6650 |
. . 3
class
((∅∈𝑔1𝑜)∧𝑔∀𝑔2𝑜((2𝑜∈𝑔1𝑜)
→𝑔
∃𝑔∅((2𝑜∈𝑔∅)∧𝑔(∅∈𝑔1𝑜)))) |
| 16 | 15, 3 | cgox 31334 |
. 2
class
∃𝑔1𝑜((∅∈𝑔1𝑜)∧𝑔∀𝑔2𝑜((2𝑜∈𝑔1𝑜)
→𝑔 ∃𝑔∅((2𝑜∈𝑔∅)∧𝑔(∅∈𝑔1𝑜)))) |
| 17 | 1, 16 | wceq 1483 |
1
wff AxInf =
∃𝑔1𝑜((∅∈𝑔1𝑜)∧𝑔∀𝑔2𝑜((2𝑜∈𝑔1𝑜)
→𝑔 ∃𝑔∅((2𝑜∈𝑔∅)∧𝑔(∅∈𝑔1𝑜)))) |
